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- Using charge qubits to facilitate the teaching of matrix mechanics
- TU Tao, LI Chuan-feng, GUO Guang-can
- College Physics. 2021, 40(12): 1. doi:10.16854 / j.cnki.1000-0712.210108
- Abstract ( 400 ) PDF (386KB) ( 603 )
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- Ab initio atomistic thermodynamics method and analysis of reaction phase diagrams
- CHU Xing-li, ZHANG Yan-xing, DU Ai-hui
- College Physics. 2021, 40(12): 8. doi:10.16854 / j.cnki.1000-0712.210185
- Abstract ( 286 ) PDF (351KB) ( 104 )
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- Calculation of volume at both ends of liquid bridge between two parallel plates
- YANG Li, CHEN Zhen-yu, XIAO Hua-peng
- College Physics. 2021, 40(12): 12. doi:10.16854 / j.cnki.1000-0712.210220
- Abstract ( 220 ) PDF (294KB) ( 72 )
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- The influence of coaxial iron tube and its defects on axial magnetic field in excitation solenoid
- MA Feng-xiang, CHU Wei, WANG Xin-yue
- College Physics. 2021, 40(12): 15. doi:10.16854 / j.cnki.1000-0712.210298
- Abstract ( 219 ) PDF (204KB) ( 67 )
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- Acousto-optic diffraction of plane light wave with spherical acoustic wave
- XI Feng, HU Li
- College Physics. 2021, 40(12): 20. doi:10.16854 / j.cnki.1000-0712.200544
- Abstract ( 213 ) PDF (266KB) ( 110 )
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- Numerical simulation of aperture diffraction with arbitrary brightness
- FANG Hui-wen, YANG Jin-hong, HE Sheng-nan, WEI Yu-jiao, ZHANG Wu-ji, WANG Wei-hua
- College Physics. 2021, 40(12): 24. doi:10.16854 / j.cnki.1000-0712.210128
- Abstract ( 241 ) PDF (468KB) ( 90 )
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- The experimental test of Born's rule
- JIN Fang-zhou, PENG Yu-ping, LI Qing-rong, ZHU Xiao-fei
- College Physics. 2021, 40(12): 29. doi:10.16854 / j.cnki.1000-0712.210030
- Abstract ( 222 ) PDF (323KB) ( 72 )
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- Theoretical analysis for the influence of particles inside the flue to beam quality
- LIU Jian-ping, FU Ji-zheng, LIN Yong
- College Physics. 2021, 40(12): 33. doi:10.16854 / j.cnki.1000-0712.210165
- Abstract ( 191 ) PDF (162KB) ( 37 )
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- Discussion of uniqueness of fixed-point motion rotation axis and vectoriality of Euler angular displacement
- XU Chen-hao, ZHANG Ya-hong
- College Physics. 2021, 40(12): 36. doi:10.16854 / j.cnki.1000-0712.210223
- Abstract ( 228 ) PDF (258KB) ( 100 )
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- The landing problem of a thin cylinder
- WU Jia-yi
- College Physics. 2021, 40(12): 41. doi:10.16854 / j.cnki.1000-0712.210056
- Abstract ( 150 ) PDF (425KB) ( 105 )
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- A brief derivation of Maxwell's speed distribution function by the character of three-dimensional sphere
- SUN Yu-chen, ZHANG Zhao-long
- College Physics. 2021, 40(12): 47. doi:10.16854 / j.cnki.1000-0712. 210072
- Abstract ( 257 ) PDF (128KB) ( 127 )
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- A new relation between angular momentum and non-commutativity of different components of momentum for a charge in a magnetic field
- CHEN Jun-feng, XIE Wei-xin, WANG Xin, LIU Quan-hui
- College Physics. 2021, 40(12): 49. doi:10.16854 / j.cnki.1000-0712.210252
- Abstract ( 279 ) PDF (146KB) ( 92 )
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- Research on the damped motion of a small magnet falling in a metal tube
- WANG Kai-ze, TAO Xiao-ping
- College Physics. 2021, 40(12): 52. doi:10.16854 / j.cnki.1000-0712.210140
- Abstract ( 251 ) PDF (189KB) ( 182 )
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- Simple measurement of the axis distance and interpupillary distance
- ZHOU Si-ying¹, CHANG Kai-ge², MAO Sheng-chun², GAO Bo²
- College Physics. 2021, 40(12): 55. doi:10.16854 / j.cnki.1000-0712.210044
- Abstract ( 415 ) PDF (708KB) ( 67 )
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- A rough measurement of s- and p-quantum defects of Sodium based on general physical experiments
- DING You-ye, ZHANG San-jun, YIN Ya-ling
- College Physics. 2021, 40(12): 62. doi:10.16854 / j.cnki.1000-0712.210080
- Abstract ( 305 ) PDF (241KB) ( 63 )
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- Optimized algorithm for arbitrary point levitation in ultrasonic phased arrays
- HUANG Jun-kang¹, DENG Kai-xiao¹, FAN Qian-qian¹, LIN Jia-hong¹, HE Qing-lin¹, PENG Li¹, ²
- College Physics. 2021, 40(12): 67. doi:10.16854 / j.cnki.1000-0712.210107
- Abstract ( 195 ) PDF (1036KB) ( 42 )
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- Investigation of stability conditions for falling tower
- XIAO Xiang-jun¹, CHEN Ke-jian², LIU Tian-qi¹
- College Physics. 2021, 40(12): 74. doi:10.16854 / j.cnki.1000-0712.210076
- Abstract ( 388 ) PDF (705KB) ( 177 )
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The representation and calculation of matrix mechanics is a very important
element

in the quantum mechanics course. The two-level system serves as a simple example to deepen

students' understanding of matrix me- chanics. However，the current textbooks give rather limited

attention to the two-level system. In this paper，we intro- duce a system in the research frontier

of quantum information: the charge qubit. In the teaching，the system is first modeled using a

Hamiltonian operator to describe the occupation and tunneling processes of a single electron in two

quantum dots. Then，the state and the time evolution of the system are obtained by three methods

such as energy ei- genfunctions representation，solving the time-dependent Schrödinger equation and

solving the equation of motion for the expectation value of an operator. Finally，by comparing the

theoretical analysis and experimental results，students can find that the theory is consistent with

the experiment. Thus these teaching contents can help students to grasp more intuitively

and deeply the quantum mechanical laws and calculations with the matrix mechanics representation.

Equilibrium conditions and equilibrium properties of multiphase systems are

important contents in thermodynamics teaching. In order to make students understand the

basic theory and the knowledge of thermody- namics deeply，the ab initio atomistic

thermodynamics method based on principle of phase equilibrium is analyzed in detail，and the

corresponding academic research results are introduced into teaching，which not only help to improve

students'understanding and application of thermodynamic equilibrium properties，but also provide a

certain reference for design of teaching contents.

When a small amount of liquid is adsorbed on two solid surfaces with tiny
spacing，the

phenomenon of liquid bridge occurs. In this paper，the liquid bridge between two narrow and long

flat plates is taken as the re- search object，and the three-dimensional liquid bridge model is established to calculate the saddle-shaped liquid volume at both ends of the liquid bridge.The relationship between the characteristic parameters of the liquid bridge shape and the volume is obtained.

On the basis of Hall effect measurement of magnetic field in excitation

solenoid，the experimentalcontent of magnetic field measurement was expanded in this article by placing an iron tube

coaxially in solenoid. Ex-perimental result showed that the intact iron tube in excitation solenoid hac almost

zero internal magnetic field. However，if the iron tube had material defects，an obvious magnetic

leakage signal could be measured at the corre- sponding axis position. This extended experiment

not only strengthens the experimental training of magnetic field measurement，but also enriches the basic experimental techniques of magnetic shielding and defect magnetic flux leakage detection.

The acousto - optic interaction of plane light wave with spherical acoustic
in

spherical cavity with open ends is investigated theoretically and experimentally. On basis

of the diffraction theory of light，the intensity distribution of diffracted light is

deduced. And then，an image of the diffracted light is displayed by numerical calcu- lation. On the

other aspect，the acousto-optic diffraction is measured with our apparatus. The measured wavelength

of acoustic wave is coincided with that of excited spherical acoustic wave.

Based on Matlab software platform，the Huygens Fresnel formula is processed
by

programming. The brightness values of various aperture light sources are realized by using

picture pixels，and the complex amplitude distribution on the light screen is calculated by

Matlab cycle. The numerical simulation of near-field / far-field dif- fraction pattern of

arbitrary shape and brightness aperture can be realized simply and quickly，and the

diffraction pattern of arbitrary shape and brightness aperture are given. In the process of

near-field diffraction to far-field dif- fraction，the change of central light intensity

gradually decreases ( from Fresnel diffraction to Fraunhofer diffrac- tion) ; in the

process of simulating the diffraction characteristics of regular polygon hole，it is verified that

when the number of regular polygon edges tends to infinity，the diffraction image is

circular hole diffraction; finally，a nu- merical example is given for diffraction pattern of

arbitrary shape and brightness hole.

Born's rule is one of the basic assumptions of quantum mechanics. It establishes a
direct correspon- dence between the mathematical form of quantum mechanics and experimental
measurement. However，some gener-alized quantum theories have proposed amendments to Born's rule， allowing the existence of multi - order interference terms. Recently，many researchers have tested Born's rule on different experimental systems，and the results obtained are consistent with Born's rule predictions within the error. This article introduces the methods of Born rule in optical and spin systems，and then proposes an improved method in spin system from the perspective of changing the observable. We hope that it is helpful for the understanding and research of Born rules in the future.

Optical method for measurement of particulate concentration in flue basing on optical
scintillation is an important non-intrusive technology. In order to research the influence of
particles to optical intensity，the inten- sity degradation of probing beam is simulated basing on
Lambert-Beer's law，when particle size distribution satisfies logarithm normal distribution and
Gauss distribution，respectively. In the calculation，the relationship between ex- tinction
coefficient and species and the middle level diameters are pre-calculated. The results show
that，when the particle size distribution satisfies logarithm normal distribution，the intensity
degradation of probing beam is more significantly. The optical intensity exhibites the same
changes when the particle size decreases gradually.

The purpose of this paper is to rigorously prove the uniqueness of the equivalent
and instantaneous rotation axes of the fixed-point motion of a rigid body by the
analytical method，and to investigate the conditions under which the Euler angular
displacement vectoriality of the fixed-point motion holds. The uniqueness of the e-
quivalent axis is proved by using the properties of the transition matrix and its eigenvector，and
on this basis，it is proved that the finite Euler angular displacement is not a vector. Then
the uniqueness of the instantaneous axis is proved，and based on the differential operation of
the transition matrix，it is concluded that the infinitesimal Euler angular displacement is a
vector，and the analytic relationship between the direction vector of the instantaneous axis and the
Euler angle is given. The rigorous proof and analysis of the conclusions related to the
fixed-point motion based on matrix operations enrich and improve the description of the
fixed-point motion of a rigid body，and the proof and analysis process further demonstrate the
advantages of matrices and their eigenvalue properties in the anal- ysis of complex rigid body
motion.

The landing problem of a thin cylinder is abstracted from the spinning-landing process of
a washba- sin or a round plate in everyday life. This problem is analytically difficult but has a fascinating physical picture. In this paper，different approximate methods are used to
gradually characterize the actual situation. The motion is shown using numerical simulation. The initial motion of a thin cylinder before it falls onto the ground can be approx-imated as a fixed point rotation and in good agreement with the reality，however，the whole motion is not fix point rotation completely. So the general motion of this rigid is studied which leads to
interesting results. The initial angu- lar velocity of precession and nutation sculptured the state of motion，while force of friction plays a vital role in cau- sing energy loss of the system.

In this paper，Maxwell's speed distribution function is derivated by using the character
of three-di- mensional sphere and the relation between the Maxwell's velocity distribution and
the Maxwell's speed distribution without solving any partial differential equations.

It is known that for a charge particle in a magnetic field，the Poisson bracket or
commutator of dif- ferent components of the momentum is proportional to a component of the magnetic
field.It is demonstrated that it is proportional a component of the mechanical angular momentum.
This new relation can be considered as a manifesta- tion of Maxwell's qualitative statement that
magnetism is essentially rotational in nature.

The paper quantitatively studies the motion of the small magnet falling on the metal

tube，gives the relevant theoretical formulas，and designs experiments that measure physical

parameters such as the falling speed of the small magnet，the magnetic moment of the small magnet

and the resistivity of the metal tube.

If the interpupillary distance does not match the axis distance of one's glasses，the

scene would be deformed，distorted and blurred，and this could result in visual fatigue and

irreversible damage to the eyes. In this paper a measurement scheme by using laser pen，ruler and

mobile phone is proposed. By analyzing the principle of optical imaging，the measurement models of

axis distance in four position cases of laser pen are established，and the calculation formulas of

two glasses with the same or the different degrees are given. Then a platform is built to do ex-

periment，and the factors affecting on the accuracy are analyzed. Tracker video analysis software is

also used to fur- ther reduce the measuring error. Finally，through taking pictures by using mobile

phone，the interpupillary distance is accurately measured. Thus conveniently measuring the

interpupillary distance and the axis distance and accurately judging whether they match or not are

realized.

The adjustment of spectrometer and measurement of the prism's refrective index is a classic，general

physical experiment. In this experiment，students can directly see the Mercury spectrum

through prisms，which is vivid，while they do not explore the formation mechanism of atom spectrual lines. On the

contrary，the experiment of Sodium spectrum is a classic，modern physical experiment. Students

understand the nature of atoms and spectrual lines through the calculation of quantumn defects and

the drawing of energy level figures. This experiment combines the thoughts of these two experiments，where students first observe spectrual lines with familiar spectrometers，and calculate the s-and p-quantum defects of Sodium with interpolation methods to understand the characteristics of at- oms. The results ( 1.348 and 0.882，respectively) are in line with the ones carefully calculated，proving that this i- dea is rather practical.

The optimization degree of the phase delays of the transducers directly affects the

precision degree of particle manipulation by the ultrasonic phased arrays. In this paper，an

improved adaptive genetic algorithm is proposed to optimize the phase delay of each transducer

in ultrasonic phased arrays. The algorithm not only has the characteristics of fast

convergence，stable convergence and good optimization effect，but also is insensitive to array size.

Four levitation points in the space are taken as examples to verify that the algorithm

has a good optimization effect on arbitrary levitation points in the space. The reliability of the algorithm is verified by

building acoustic levi- tation experiment of ultrasonic phased arrays to conduct levitation

experiments.

Identical discs are stacked one on top of another to form a freestanding tower. The

bottom disc can be removed by applying a sudden horizontal force such that the rest of the

tower will drop down onto the surface and the tower remains standing. Investigate the phenomenon

and determine the conditions that allow the tower to remain standing. Theoretically，the dynamic

analysis is carried out by stages，and it is found that the key to judge whether the tower collapses

lies in the position of the tower at the moment when it hits the ground. In the experiment，the ro-

tating shaft of the motor is used to drive the rope to pull the disc to exert horizontal

force，which improves the con- trollability and repeatability of the experiment. The effects of the

height of the horizontal force point，the ratio of the disc thickness to the radius and the number

of layers on the stability of the tower are investigated. The theoretical and

experimental trends are in good agreement，and the differences between them are analyzed and

explained.